Friday, July 12, 2013

1307.3111 (Ferdinando Gliozzi)

More constraining conformal bootstrap    [PDF]

Ferdinando Gliozzi
It has been recently developed an efficient numerical method to implement the constraints of crossing symmetry and unitarity on the operator dimensions and OPE coefficients of conformal field theories in various space-time dimensions. It appears that the calculations can be actually done only for theories lying at the boundary of the allowed parameter space. Here it is pointed out that a similar method can be applied to a larger class of CFT's, whether unitary or not, and no free parameter is left, provided we know the fusion algebra of the low lying primary operators. As an example we calculate from the first principles, with no phenomenological input, the lowest scaling dimensions of the local operators associated to the Yang-Lee edge singularity in three dimensions. The edge exponent compares favorably with the latest numerical estimates. A consistency check of this approach on the 3d critical Ising model is also made.
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